MATH 162:Philosophy of Mathematics (PHIL 162)

Mathematics is a very peculiar human activity. It delivers a type of knowledge that is particularly stable, often conceived as a priori and necessary. Moreover, this knowledge is about abstract entities, which seem to have no connection to us, spatio-temporal creatures, and yet it plays a crucial role in our scientific endeavors. Many philosophical questions emerge naturally: What is the nature of mathematical objects? How can we learn anything about them? Where does the stability of mathematics comes from? What is the significance of results showing the limits of such knowledge, such as Gödel's incompleteness theorem? The first part of the course will survey traditional approaches to philosophy of mathematics ("the big Isms") and consider the viability of their answers to some of the previous questions: logicism, intuitionism, Hilbert's program, empiricism, fictionalism, and structuralism. The second part will focus on philosophical issues emerging from the actual practice of mathemat
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Mathematics is a very peculiar human activity. It delivers a type of knowledge that is particularly stable, often conceived as a priori and necessary. Moreover, this knowledge is about abstract entities, which seem to have no connection to us, spatio-temporal creatures, and yet it plays a crucial role in our scientific endeavors. Many philosophical questions emerge naturally: What is the nature of mathematical objects? How can we learn anything about them? Where does the stability of mathematics comes from? What is the significance of results showing the limits of such knowledge, such as Gödel's incompleteness theorem? The first part of the course will survey traditional approaches to philosophy of mathematics ("the big Isms") and consider the viability of their answers to some of the previous questions: logicism, intuitionism, Hilbert's program, empiricism, fictionalism, and structuralism. The second part will focus on philosophical issues emerging from the actual practice of mathematics. We will tackle questions such as: Why do mathematicians re-prove the same theorems? What is the role of visualization in mathematics? How can mathematical knowledge be effective in natural science? To conclude, we will explore the aesthetic dimension of mathematics, focusing on mathematical beauty. Prerequisite: PHIL150 or consent of instructor.

PHIL 23B:Truth and Paradox

Philosophical investigation of the concept of truth is often divided along two dimensions: investigation of the nature of truth and investigation of the semantics of truth claims. This tutorial will focus on the second kind of concern. One key impetus for a philosophical interest in the semantics and definability of truth is the challenge posed by semantic paradoxes such as the Liar paradox and Curry¿s paradox. Despite each having the initial appearance of a parlor trick, philosophers and logicians have come to appreciate the deep implications of these paradoxes. The main goal of this tutorial is to gain an appreciation of the philosophical issues -­ both with respect to formal and natural languages ­¿ which arise from consideration of the paradoxes. To this end, we will study some of the classic contributions to this area including Tarski¿s famous result that, in an important sense, the semantic paradoxes render truth indefinable, and Kripke¿s much later attempt to provide a definitio
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Philosophical investigation of the concept of truth is often divided along two dimensions: investigation of the nature of truth and investigation of the semantics of truth claims. This tutorial will focus on the second kind of concern. One key impetus for a philosophical interest in the semantics and definability of truth is the challenge posed by semantic paradoxes such as the Liar paradox and Curry¿s paradox. Despite each having the initial appearance of a parlor trick, philosophers and logicians have come to appreciate the deep implications of these paradoxes. The main goal of this tutorial is to gain an appreciation of the philosophical issues -­ both with respect to formal and natural languages ­¿ which arise from consideration of the paradoxes. To this end, we will study some of the classic contributions to this area including Tarski¿s famous result that, in an important sense, the semantic paradoxes render truth indefinable, and Kripke¿s much later attempt to provide a definition of truth in the face of Tarski¿s limitative result. Further topics include the debate between paracomplete and paraconsistent solutions to the semantic paradoxes (notably defended by, respectively, Field and Priest); the relationship between deflationism about truth and the paradoxes; and the notion of ¿revenge problems¿ (roughly, the claim that any solution to the paradoxes can be used to construct a further paradox).nThe tutorial will avoid excessive technical discussions, but will aim to engender appreciation for some philosophical interesting technical points and will assume a logic background of PHIL150 level.

Terms: not given this year
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Units: 2
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Grading: Satisfactory/No Credit

PHIL 150:Mathematical Logic (PHIL 250)

An introduction to the concepts and techniques used in mathematical logic, focusing on propositional, modal, and predicate logic. Highlights connections with philosophy, mathematics, computer science, linguistics, and neighboring fields.

PHIL 150E:Logic in Action: A New Introduction to Logic

A new introduction to logic, covering propositional, modal, and first-order logic, with special attention to major applications in describing information and information-driven action. Highlights connections with philosophy, mathematics, computer science, linguistics, and neighboring fields. Based on the open source course 'Logic in Action,' available online at
http://www.logicinaction.org/.nFulfills the undergraduate philosophy logic requirement.

PHIL 150X:Mathematical Logic

Equivalent to the second half of 150. Students attend the first meeting of 150 and rejoin the class on October 30. Prerequisite:
CS 103A or X, or
PHIL 50.

Terms: not given this year
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Units: 2
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Grading: Letter or Credit/No Credit

PHIL 162:Philosophy of Mathematics (MATH 162)

Mathematics is a very peculiar human activity. It delivers a type of knowledge that is particularly stable, often conceived as a priori and necessary. Moreover, this knowledge is about abstract entities, which seem to have no connection to us, spatio-temporal creatures, and yet it plays a crucial role in our scientific endeavors. Many philosophical questions emerge naturally: What is the nature of mathematical objects? How can we learn anything about them? Where does the stability of mathematics comes from? What is the significance of results showing the limits of such knowledge, such as Gödel's incompleteness theorem? The first part of the course will survey traditional approaches to philosophy of mathematics ("the big Isms") and consider the viability of their answers to some of the previous questions: logicism, intuitionism, Hilbert's program, empiricism, fictionalism, and structuralism. The second part will focus on philosophical issues emerging from the actual practice of mathemat
more »

Mathematics is a very peculiar human activity. It delivers a type of knowledge that is particularly stable, often conceived as a priori and necessary. Moreover, this knowledge is about abstract entities, which seem to have no connection to us, spatio-temporal creatures, and yet it plays a crucial role in our scientific endeavors. Many philosophical questions emerge naturally: What is the nature of mathematical objects? How can we learn anything about them? Where does the stability of mathematics comes from? What is the significance of results showing the limits of such knowledge, such as Gödel's incompleteness theorem? The first part of the course will survey traditional approaches to philosophy of mathematics ("the big Isms") and consider the viability of their answers to some of the previous questions: logicism, intuitionism, Hilbert's program, empiricism, fictionalism, and structuralism. The second part will focus on philosophical issues emerging from the actual practice of mathematics. We will tackle questions such as: Why do mathematicians re-prove the same theorems? What is the role of visualization in mathematics? How can mathematical knowledge be effective in natural science? To conclude, we will explore the aesthetic dimension of mathematics, focusing on mathematical beauty. Prerequisite: PHIL150 or consent of instructor.

PHIL 351D:Measurement Theory

What does it mean to assign numbers to beliefs (as Bayesian probability theorists do), desires (as economists and philosophers who discuss utilities do), or perceptions (as researchers in psychometrics often do)? What is the relationship between the numbers and the underlying reality they purport to measure? Measurement theory helps answer these questions using representation theorems, which link structural features of numerical scales (such as probabilities, utilities, or degrees of loudness) to structural features of relations (such as comparative belief, preference, or judgments that one sound is louder than another).nThis course will introduce students to measurement theory, and its applications in psychophysics and decision theory. n2 unit option only for Philosophy PhD students who are past their second year.nPrerequisites: Undergraduates wishing to take this course must have previously taken
PHIL150, and may only enroll with permission from the instructor.